The chain weighted CPI incorporates changes in both the quantities and prices of products. For example, let's examine clothing purchases between two years. Last year you bought a sweater for $40 and two t-shirts at $35 each. This year, two sweaters were purchased at $35 each and one t-shirt for $45.
Standard CPI calculations would produce an inflation level of 13.64%
((1 x 35 + 2 x 45)/ (1 x 40 + 2 x 35)) =1.1364
The chain weighted approach estimates inflation to be 4.55%
((2 x 35 + 1 x 45)/ (1 x 40 + 2 x 35)) =1.0455.
Using the chain weighted approach reveals the impact of a customer purchasing more sweaters than t-shirts.